Acceleration as a function of velocity - HW problem help

The acceleration of a particle is defined by the relation a = -0.05v^2, where a is expresssed in m/s^2 and v in m/s. The particle starts at s=0 m with a velocity of 5 m/s. Determine (a) the velocity v of the particle after it travels 10m, (b) the distance s the particle will travel before its velocity drops to 2 m/s, (c) the distance s the particle will travel before it comes to rest.

2. Relevant equations

a = v (dv/ds)

3. The attempt at a solution

I don't think this is right because when I integrated the right side, it ends up being undefined?

How can you just cancel "v" on both sides in second step , where it can take a value zero...

Easy, you just say that the step was valid for all non-zero values of v.
[tex]a=v\frac{dv}{dx}=-kv^2[/tex] (In this case, k=0.05)
From this step to the next, you have two options. Either v is always 0, in which case you have a solution for v, and you are not allowed to divide by v. Or v is different from 0, and you are allowed to divide by it.

suchara, the velocity as a function of time is not what you posted. Note that you used the expression for the velocity as a function of distance and replaced the x with t (A mistake).